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Generative Local Metric Learning for Kernel Regression
Yung-Kyun Noh · Masashi Sugiyama · Kee-Eung Kim · Frank Park · Daniel Lee

Mon Dec 04 06:30 PM -- 10:30 PM (PST) @ Pacific Ballroom #51

This paper shows how metric learning can be used with Nadaraya-Watson (NW) kernel regression. Compared with standard approaches, such as bandwidth selection, we show how metric learning can significantly reduce the mean square error (MSE) in kernel regression, particularly for high-dimensional data. We propose a method for efficiently learning a good metric function based upon analyzing the performance of the NW estimator for Gaussian-distributed data. A key feature of our approach is that the NW estimator with a learned metric uses information from both the global and local structure of the training data. Theoretical and empirical results confirm that the learned metric can considerably reduce the bias and MSE for kernel regression even when the data are not confined to Gaussian.

Author Information

Yung-Kyun Noh (Seoul National University)
Masashi Sugiyama (RIKEN / University of Tokyo)
Kee-Eung Kim (KAIST)
Frank Park (Seoul National University)
Daniel Lee (Cornell Tech)

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